• OPTIMAL HAMILTON-TYPE GRADIENT...

Result: OPTIMAL HAMILTON-TYPE GRADIENT ESTIMATES FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS

Title:
OPTIMAL HAMILTON-TYPE GRADIENT ESTIMATES FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
Authors:
Chabi, Loth Damagui, Souplet, Philippe
Contributors:
Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Publisher Information:
CCSD, 2025.
Publication Year:
2025
Collection:
collection:UNIV-PARIS13
collection:UNIV-PARIS8
collection:CNRS
collection:LAGA
collection:INSMI
collection:UNIV-PARIS-LUMIERES
collection:SORBONNE-PARIS-NORD
collection:UNIV-PARIS8-OA
collection:ACT-R
Subject Terms:
Heat equation, Riemannian manifolds, sharp gradient estimates, Harnack inequality, modulus of continuity, 35K05, 58J35, [MATH]Mathematics [math]
Original Identifier:
HAL: hal-05175053
Document Type:
Electronic Resource preprint<br />Preprints<br />Working Papers
Language:
English
Access URL:
https://hal.science/hal-05175053
https://hal.science/hal-05175053v1/document
https://hal.science/hal-05175053v1/file/2507.12190v1.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.05175053v1
Database:
HAL

Further Information

We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and significantly improve on all previous estimates of this type. As applications, we derive a new and sharp, space only, local pseudo-Harnack inequality, as well as estimates of the spatial modulus of continuity of solutions.